Toward a Restriction-Centered Theory of Truth and Meaning (RCT)
Studies in Fuzziness and Soft Computing
What is truth? The question does not admit a simple, precise answer. A dictionary-style definition is: The truth value of a proposition, p, is the degree to which the meaning of p is in agreement with factual information, F. A precise definition of truth will be formulated at a later point in this paper. The theory outlined in the following, call it RCT for short, is a departure from traditional theories of truth and meaning. In RCT, truth values are allowed to be described in natural language.
... n natural language. Examples. Quite true, more or less true, almost true, largely true, possibly true, probably true, usually true, etc. Such truth values are referred to as linguistic truth values. Linguistic truth values are not allowed in traditional logical systems, but are routinely used by humans in everyday reasoning and everyday discourse. The centerpiece of RCT is a deceptively simple concept-the concept of a restriction. Informally, a restriction, R(X), on a variable, X, is an answer to a question of the form: What is the value of X? Possible answers: X = 10, X is between 3 and 20, X is much larger than 2, X is large, probably X is large, usually X is large, etc. In RCT, restrictions are preponderantly described in natural language. An example of a fairly complex description is: It is very unlikely that there will be a significant increase in the price of oil in the near future. The canonical form of a restriction, R(X), is X isr R, where X is the restricted variable, R is the restricting relation, and r is an indexical variable which defines the way in which R restricts X. X may be an n-ary variable and R may be an n-ary relation. The canonical form may be interpreted as a generalized assignment statement in which what is assigned to X is not a value of X, but a restriction on the values which X can take. A restriction, R(X), is a carrier of information about X. A restriction is precisiated if X, R and r are mathematically well defined. A key idea which underlies RCT is referred to as the meaning postulate, MP. MP postulates that the meaning of a proposition drawn from a natural language, p-or simply p-may be represented as a restriction, p ? X isr R. This expression is referred to as the canonical form of p, CF(p). Generally, the variables X, R and r are implicit in p. Simply stated, MP postulates that a proposition drawn from a natural language may be interpreted as an implicit assignment statement. MP plays an essential role in defining the meaning of, and computing with, propositions drawn from natural language. What should be underscored is that in RCT understanding of meaning is taken for granted. What really matters is not understanding of meaning but precisiation of meaning. 0020-0255/$ -see front matter Ó